On the Laplace New Iterative Method for Modeling Fractional Positron-Acoustic Cnoidal Waves in Electron-Positron-Ion Plasmas with Kaniadakis Distributed Electrons

The propagation of high-frequency positron-acoustic cnoidal waves (PACWs) is investigated in four-component plasmas consisting of inertialess non-Maxwellian electrons and hot positrons adhering to the Kaniadakis distribution, together with inertial fluid cold positrons and stationary ions. Using the reductive perturbation approach (RPA), the quadratic planar Korteweg-de Vries (KdV) equation is derived, and its cnoidal wave (CW) solution is reported. Additionally, at a critical plasma composition, such as the hot positron concentration, the modified-KdV (mKdV) equation is derived, and its CW solution is investigated. Subsequently, to examine the distinctive behavior of the fractional PACWs, both the integer KdV and mKdV equations are transformed into their fractional counterparts, namely the fractional KdV (FKdV) and fractional mKdV (FmKdV) equations. The Laplace novel iterative method (LNIM) is utilized to solve both FKdV and FmKdV equations and derive high-accuracy approximations for the two equations for modeling the characteristic behavior of FKdV-PACWs and KmKdV-PACWs. The influence of several associated physical parameters on the profile (amplitude and width) of both KdV-PACWs and mKdV-PACWs is numerically examined. Additionally, the impact of the fractionality on the profile of both FKdV-PACWs and FmKdV-PACWs is investigated. Moreover, the absolute error of the derived approximations is estimated and discussed numerically. Furthermore, the potential applications of the current study are discussed, and the obtained results are valuable for investigating the cosmic ray spectrum and the plasma environment surrounding stars.